Question: Simplify the following expression: $ q = \dfrac{-8}{10k + 5} - \dfrac{-9}{4} $
Answer: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{4}{4}$ $ \dfrac{-8}{10k + 5} \times \dfrac{4}{4} = \dfrac{-32}{40k + 20} $ Multiply the second expression by $\dfrac{10k + 5}{10k + 5}$ $ \dfrac{-9}{4} \times \dfrac{10k + 5}{10k + 5} = \dfrac{-90k - 45}{40k + 20} $ Therefore $ q = \dfrac{-32}{40k + 20} - \dfrac{-90k - 45}{40k + 20} $ Now the expressions have the same denominator we can simply subtract the numerators: $q = \dfrac{-32 - (-90k - 45) }{40k + 20} $ Distribute the negative sign: $q = \dfrac{-32 + 90k + 45}{40k + 20}$ $q = \dfrac{90k + 13}{40k + 20}$